# Nonlinear Dynamics

## List of Papers (Total 159)

#### Reduction of dimension for nonlinear dynamical systems

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where this reduction is possible, we employ differential elimination...

#### Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

In order to obtain an isolator with low resonance amplitude as well as good isolation performance at high frequencies, this paper explores the usage of nonlinear stiffness elements to improve the transmissibility efficiency of a sufficient linear damped vibration isolator featured with the Zener model. More specifically, we intend to improve its original poor high-frequency...

#### Switching processes in polynomiography

Mandelbrot and Julia sets are examples of fractal patterns generated in the complex plane. In the literature, we can find many generalizations of those sets. One of such generalizations is the use of switching process. In this paper, we introduce some switching processes to another type of complex fractals, namely polynomiographs. Polynomiograph is an image presenting the...

#### Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment

The transverse vibration of an elastic disc, excited by a preloaded mass–damper–spring slider dragged around on the disc surface at a constant rotating speed and undergoing in-plane stick–slip oscillation due to friction, is studied. As the vertical vibration of the slider grows at certain conditions, it can separate from the disc and then reattach to the disc. Numerical...

#### Targeted energy transfer and modal energy redistribution in automotive drivetrains

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure...

#### Nonlinear predictive control of dynamic systems represented by Wiener–Hammerstein models

This paper is concerned with computationally efficient nonlinear model predictive control (MPC) of dynamic systems described by cascade Wiener–Hammerstein models. The Wiener–Hammerstein structure consists of a nonlinear steady-state block sandwiched by two linear dynamic ones. Two nonlinear MPC algorithms are discussed in details. In the first case the model is successively...

#### Continuation techniques for analysis of whole aeroengine dynamics with imperfect bifurcations and isolated solutions

The analysis of whole engine rotordynamic models is an important element in the design of aerojet engines. The models include gyroscopic effects and allow for rubbing contact between rotor and stator components such as bladed discs and casing. Due to the nonlinearities inherent to the system, bifurcations in the frequency response may arise. Reliable and efficient methods to...

#### Nonlinear vibrations of a misaligned bladed Jeffcott rotor

This paper describes the numerical and experimental investigation of the nonlinear vibration of a bladed Jeffcott rotor. The nonlinearity in the system is due to discontinuities caused by multiple contacts with an outer ring as well as the nonlinear deformation of the massless blades. Contacts occur since the rotor shaft is initially misaligned by displacing the outer ring in one...

#### A fast sampling method for estimating the domain of attraction

Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DoA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate...

#### The quadratically cubic Burgers equation: an exactly solvable nonlinear model for shocks, pulses and periodic waves

A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and...

#### Dynamics of kinky wave for ( $3+1$ )-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Exact kinky breather-wave solutions for the ($3\,{+}\,1$)-dimensional potential Yu–Toda–Sasa–Fukuyama equation are obtained by using extended homoclinic test technique. Based on the kinky breather-wave solution, rational breather-wave solution is generated by homoclinic breather limit method. Some new dynamical features of kinky wave are presented, including kink degeneracy...

#### Dynamically consistent Jacobian inverse for non-holonomic robotic systems

This paper presents an extension of the concept of dynamically consistent Jacobian inverse from robotic manipulators (holonomic systems) to non-holonomic robotic systems, like mobile robots. This new inverse is derived within the framework of the endogenous configuration space approach, following a strict analogy with the original derivation of the dynamically consistent Jacobian...

#### Application of dynamic optimisation to the trajectory of a cable-suspended load

The paper discusses a dynamic model of the system consisting of an on-board hoisting winch on a moving vessel, cable, and load. The model accounting for large rope sag and hydrodynamic drag force was used to solve the problem of dynamic optimisation. The essence of which is what angle of rotation should be selected for the hoisting winch to ensure that the load during the defined...

#### Research on chaos and nonlinear rolling stability of a rotary-molded boat

On the basis of nonlinear features analysis of restoring torque, damping torque and especially hull deformation, a nonlinear roll equation of rotary-molded boats has been established. The equation includes elastic deformation term which makes the equation different from existing ones for steel boats. This paper dissected its dynamic characteristic of rolling motion from different...

#### Nonlinear reduced-order modelling for limit-cycle oscillation analysis

A nonlinear model reduction based on eigenmode decomposition and projection for the prediction of sub- and supercritical limit-cycle oscillation is presented herein. The paper focuses on the derivation of the reduced-order model formulation to include expansion terms up to fifth order such that higher-order nonlinear behaviour of a physical system can be captured. The method is...

#### $N-1$ modal interactions of a three-degree-of-freedom system with cubic elastic nonlinearities

In this paper the $N-1$ nonlinear modal interactions that occur in a nonlinear three-degree-of-freedom lumped mass system, where $N=3$, are considered. The nonlinearity comes from springs with weakly nonlinear cubic terms. Here, the case where all the natural frequencies of the underlying linear system are close (i.e. \(\omega _{n1}: \omega _{n2}:\omega _{n3} \approx 1:1:1...